{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 15 - State Minimization-2x2(1)

Chapter 15 - State Minimization-2x2(1) - Table 15-1 State...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
.ROSOTPZOUT Uu 7ts[TsPTZ 8ZPZtY Unit ±²³ avoided introducing unnecessary states when setting up a state graph used hoc approach Will now derive state graph somewhat differently³ Will not be overly concerned with redundant states instead when table is complete´ will eliminate redundant statesµ Rework (xample ± in Section ±²µ¶ using redundant states´ and then eliminate them 8trZOUT ±²³± ´V³ µ¶µ· 9PQRt ±²¸±¹ 8ZPZt 9PQRt uUX 8tW[tTrt -tZtrZUX 9PQRt ±²¸º³ 8ZPZt 9PQRt uUX 8tW[tTrt -tZtrZUX Since states / and 0 have the same next states and the same outputs´ there is no way of telling states / and 0 apart´ and we can replace 0 with / µ )NMZWK !%±!T* Reduced State Table for Sequence Detector
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
)NMZWK !%±!H* Reduced State Graph for Sequence Detector Notation± *iven netlist N² state s² input sequence X ² denote output sequence by L³s² X ´ -TUOtOZOut µ¶·µ± Let 4 µ and 4 ¸ be sequential circuits ³ not necessarily different´ Let = represent a sequence of inputs of arbitrary length· Then state U in 4 µ is equivalent to state V in 4 ¸ iff Lµ³ U ² = ´" L¸³ V ² = ´ for every possible input sequence = · )NMZWK !%±" .W[O\PRTtZ 8ZPZTY 9wTuXTS ±²³± ± Two states U and V of a sequential circuit are equivalent iff for every single input = ² the outputs are the same and the next states are equivalent Mathematically² L³p²X´ " L³q²X´ and d³p²X´ d ³q²x´ where L³ U ² = ´ is output for present state U and input = ² and d³ U ² = ´ is next state for present state U and input = · 2´5479*39 ± the next states do not have to be equal² just equivalent· 9PQRT ±²µ¶³ -TZTXSOtPZOut uU 8ZPZT .W[O\PRTtrT P ⟨ Q OUU s ⟨ U Pts r ⟨ w P ⟨ s OUU P ⟨ s Pts r ⟨ T
Image of page 2
)NMZWK !%±#* Implication Chart for Table !%±# )NMZWK !%±$* Implication Chart $fter First Pass )NMZWK !%±%* Implication Chart $fter Second Pass 9PQRT ±²³´µ ,f we replace I with F and J with H in Table ±²³´µ we can eliminate rows I and J µ and the table reduces to six rows¶
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2SVROrPZOUT 9PQRt ±tZWUs 8trZOUT ²³´µ ¶V´ ·¸²¹ The implication table method for finding equivalent states can be summarized as follows± ²³ &onstruct chart containing a square for each pair of states³
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern